Radiation on the Transmission of Heat. 251 



by combining the two first equations of (19) with (18). We 

 then find 



2aR(l + o-) = \a[«(l + -)(P-Q)-a(l-o-)(P + Q)]. . (22) 



I will consider the two extreme cases <r = () and <7=1 in 

 greater detail. For cr = Q : 



2dR*X4*(P^Q)-«(P + Q)], . . . (22a) 



for <r = l : 



2aR = \*fc{F-Q) (22 h) 



The values o£ P and a, as found from the combination of 

 (20), (2J), and either (22 a) or (22 b), are as follows :— 

 For <r = 0: 



- _ U** [*(«"* + 1)4- a(e at —l) ] 



2RU 



(m + \xH)(e at -l) + }ucKt(e at +l)' ' ' ™ 4a ) 



For ff =l : 



UXatf^+l) 



(23 a) 



1R (^ - 1) + XaKt(e at + 1) 

 2RU 



(23 &) 



(24 6) 



4R(^-l)+\a**(^'+l) * ■ * 



In order to show the characteristics o£ the temperature 

 variation indicated by (12) I have plotted curves, taking 

 for k the value of '61 and putting X = l-3xl0 _1 . A body 

 possessing these constants would have the transparency of 

 clear rock-salt, and a thermal conductivity equal to that of cork. 

 I have calculated the appropriate value of R by taking the 

 radiation of a black body per unit surface to be 10 -1 - x u\ 

 where u is the absolute temperature. This is in close agree- 

 ment with the best observations. Two black parallel surfaces 

 differing in temperature by a small amount du, exchange 

 heat therefore at the rate of 4x 10~ l2 u 3 du. If u is equal 

 to 300° on the absolute scale this will be nearly 10" 4 x du. 

 Hence for temperatures nearly equal to 30° C. we may in the 

 above equations put R=10~ 4 . 



Curve I. (PL II.) gives the temperature change in a plate of 

 a substance having the properties described, the plate being 

 5 cms. thick and placed between two totally reflecting sur- 

 faces, the average temperature being about 30° C. Curve 11. 



